Sebastian Wolf, M. Sc.

Hamilton's principle offers an elegant method for describing physical systems and goes beyond classical Newtonian mechanics. It can be applied to systems that are not only mechanical, but also thermodynamic, electromagnetic or other in character.
Through the variation of an action functional, which takes into account all forces and energies occurring in the system, physical balance equations can be derived. These equations take into account all interactions that occur and ensure thermodynamic consistency.
While this approach is widely used in classical continuum mechanics as well as in theoretical electrodynamics, which is mostly restricted to electromagnetic fields in vacuum, it does not apply to continuum models that consider electromagnetic fields. This is mainly due to the fact that Maxwell's equations for deformable bodies in the general case require consideration of the special relativity theory.
In this context, a continuum mechanical version of Hamilton's principle considering electromagnetic fields is now formulated from a relativistic approach. Two limiting cases are considered for which a non-relativistic approach is possible. This theory will be used as a basis for a numerical topology optimisation.